What is eager learning and lazy learning?
What is eager learning or lazy learning?

Eager learning is when a model does all its computation before needing to make a prediction for unseen data. For example, Neural Networks are eager models.
Lazy learning is when a model doesn't require any training, but all of its computation during inference. An example of such a model is k-NN. Eager learning is also known as instance-based learning [1, 2, 3].

How does eager and lazy learning help me build a neural network system? And how can I use it for any target function?

To answer your second question, you can't employ lazy learning to train a neural network, because they are inherently eager models.